Lock a background image from being easily deleted?
There is a way if you are willing to edit Python files in the Blender installation... Go to to the directory Blender/2.78/scripts/startup/bl_ui and edit the file space_view3d.py in a text editor (after you made a backup)

Search for the line

row.operator("view3d.background_image_remove", text="", emboss=False, icon='X').index = i


This is the code that adds the delete button. Add the following line in the front of it:

row.label(text="  ") 


This line adds an (invisible) text consisting of two spaces between the eye icon and the delete button. You can change the number of spaces as you like. Result:



And in the future when you upgrade your Blender version, repeat the procedure. Not very convenient, I know :)